Thanks. In short, this is the proposed change. Taking this:

if (JX.RemarkupMetadata._metadataValue == null) {
  JX.RemarkupMetadata._metadataValue = [];
  JX.RemarkupMetadata._metadataValue[metadataID] = metadataValue;
} else if (!JX.RemarkupMetadata._metadataValue.hasOwnProperty(metadataID)) {
  JX.RemarkupMetadata._metadataValue[metadataID] = metadataValue;
}

And simplifying it to this:

if (JX.RemarkupMetadata._metadataValue == null) {
  JX.RemarkupMetadata._metadataValue = {};
}
if (!JX.RemarkupMetadata._metadataValue.hasOwnProperty(metadataID)) {
  JX.RemarkupMetadata._metadataValue[metadataID] = metadataValue;
}

Reasons:

1. I suggest to have myVar = {} instead of myVar = [] (so, explicitly declaring an object, instead of an array-object) since using a JavaScript array-object for an "associative map" is a little understood hack, and the risk here is that a person with experience in PHP misunderstand what is going on in JavaScript, and he/she can goes crazy when he/she finds out that things like .length are completely broken on the array, since we are not really working with an array, we are really not adding elements to an array, etc. Here we need an "associative array", and since in JavaScript an array is really an object, and since the syntax myVar['foo']=value just does myVar.foo=value on an object, and since hasOwnProperty() is just inherited from the generical object class, I suggest to just declare it as any normal object. I'm sincerely sorry if JavaScript is so weird. If you have a doubt, think about JSON: an "associative array" is just an object {}, while arrays are only used to represent a stack of consecutive elements.
2. I also suggest to avoid the base case optimization, essentially because it does not justify the loss of readability. It also avoids the introduction of future typos since we don't repeat the same instruction twice.